The progression went like this
- Chainmail was a set of rules for wargaming with miniatures.
- People wanted to fight the battles they read about in Lord of the Rings, Conan, and other fantasy novels of the time. So the Fantasy Supplement was added.
- Dave Arneson was inspired by David Wesley Braunstein game to create his own version. He used the Man to Man and Fantasy Supplement Rules of Chainmail as the foundation of his rules. The scenario he picked was exploring the dungeon underneath Castle Blackmoor and later the surrounding Wilderness.
- Gygax and his friends from Lake Geneva found out about this and went to Minnepolis to play a few sessions of Dave's Game.
- Gygax started his Castle Greyhawk campaign with it's own dungeon and wilderness and wrote what was to be the Dungeons & Dragons rules.
- The Dungeons & Dragons rules were written with knowledge of Chainmail in mind but presented alternatives in order to use it as a Standalone game.
- Greyhawk Supplement I expanded and added rules that transformed the game into the D&D most of us recognize today.
The design choices were mainly in making Chainmail rules more interesting for man to man combat. Chainmail's 1 hit = 1 kill was transformed 1 hit = 1d6 damage, 1 level = 1d6 hit points. The Alternative combat system used a chart indexing level vs Armor Class instead of Chainmail's weapon vs Armor matrix or Creature vs Creature matrix. Spells and the Monster list were expanded. An equipment list was added. The focus of the original game was on dungeon crawling, and the exploration of the wilderness. Plus since this was a group of miniature wargamers rules for constructing castles and building baronies was included.
Original D&D wasn't designed as much it grew out of the piecemeal solutions to the rule problems they encountered while roleplaying their way through the campaigns of the time. While this sound haphazard it was wildly popular in both Minnepolis and Lake Geneva. They were refereeing over a dozen players a session and playing multiple times a week. So they got quite a lot of time in with developing the rules.